How to apply a real time constraint on a moving gear
Not sure if you're interested in this solution, as it does not deal with physics simulation but using traditional constraints instead. As mentioned in a few comments already, this is recommended for various reasons, like easier handling and setup, better stability, etc. For what you're really trying to achieve, this will work.

Here is the file rigged based on your provided Blend:



I'm using an Armature, parenting a few bones in there in a hierachy like this:



Main Bone and Lever Bone are purely for better flexibility later on when animating. Using the Main Bone you can relocate the whole rig, the gear bone allows additional offset. Both bones are optional, but recommended. The lever bone is a child of the Gear Bone, so it follows the movement of that, and the sprocket bone a child of the lever bone.

The rig itself looks like this:



I turned on Axis Display for each bone, so you can see the local bone axis and better understand why I set certain values later on in the Constraint. Speaking of the Constraint, I used a Transformation constraint to achieve the desired effect:



The logic is: If you rotate the lever bone by 8 degrees along the Z axis, the sprocket bone has to spin 36 degrees along the Y axis, but in the opposite direction, hence the -36 degrees. Where I got these values from? Simply count the number of teeth of gear and sprocket. The Extrapolate option makes sure that this math relationship is kept even if you exceed the values.

Now, if you rotate the red lever bone, the sprocket spins around the gear.